updated

notebooks/ml/SupportVectorMachines.ipynb

@@ -1108,7 +1108,7 @@
     "\n",
     "<img src=\"./img/svr.png\" width=600/>\n",
     "\n",
-    "Referring to this figure, the region bound by $y'_{i}\\pm\\epsilon \\ \\forall_{i}$ is called an $\\epsilon$-insensitive tube. The other modification to the penalty function is that output variables which are outside the tube are given one of two slack variable penalties depending on whether they lie above $(\\xi^{+})$ or below $(\\xi^{-})$ the tube (where $\\xi^{+}>0, \\xi^{-}>0 \\ \\forall_{i}$):\n",
+    "Referring to this figure, the region bound by $y'_{i}\\pm\\epsilon \\ \\forall_{i}$ is called an $\\epsilon$-insensitive tube. The other modification to the penalty function is that output variables which are outside the tube are given one of two slack variable penalties depending on whether they lie above $(\\xi^{+})$ or below $(\\xi^{-})$ the tube (where $\\xi^{+} \\geq 0, \\xi^{-} \\geq 0 \\ \\forall_{i}$):\n",
     "\n",
     "$$\n",
     "\\begin{equation}\n",

optiml/ml/svm/_base.py

@@ -12,7 +12,7 @@
 from .smo import SMO, SMOClassifier, SMORegression
 from ...opti import Optimizer
 from ...opti import Quadratic
-from ...opti.qp import LagrangianEqualityConstrainedQuadratic, LagrangianConstrainedQuadratic
+from ...opti.qp import LagrangianConstrainedQuadratic
 from ...opti.qp.bcqp import BoxConstrainedQuadraticOptimizer, LagrangianBoxConstrainedQuadratic
 from ...opti.unconstrained import ProximalBundle
 from ...opti.unconstrained.line_search import LineSearchOptimizer
@@ -357,12 +357,9 @@ def fit(self, X, y):
 
                 if issubclass(self.optimizer, BoxConstrainedQuadraticOptimizer):
 
-                    self.obj = LagrangianEqualityConstrainedQuadratic(Q, q, A)
-                    self.optimizer = self.optimizer(f=self.obj, ub=np.append(ub, 0), max_iter=self.max_iter,
-                                                    verbose=self.verbose)
-                    self.optimizer.x = np.zeros(self.obj.ndim)
-                    self.optimizer.minimize()
-                    alphas = self.optimizer.x[:-1]
+                    self.optimizer = self.optimizer(f=self.obj, ub=ub, max_iter=self.max_iter,
+                                                    verbose=self.verbose).minimize()
+                    alphas = self.optimizer.x
 
                 elif issubclass(self.optimizer, Optimizer):
 

optiml/opti/qp/__init__.py

@@ -1,3 +1,3 @@
-__all__ = ['LagrangianDual', 'LagrangianEqualityConstrainedQuadratic', 'LagrangianConstrainedQuadratic']
+__all__ = ['LagrangianDual', 'LagrangianConstrainedQuadratic']
 
-from .lagrangian_dual import LagrangianDual, LagrangianEqualityConstrainedQuadratic, LagrangianConstrainedQuadratic
+from .lagrangian_dual import LagrangianDual, LagrangianConstrainedQuadratic

optiml/opti/qp/lagrangian_dual.py

@@ -84,31 +84,6 @@ def callback(self, args=()):
             self._callback(self, *args, *self.callback_args)
 
 
-class LagrangianEqualityConstrainedQuadratic(Quadratic):
-
-    def __init__(self, Q, q, A):
-        """
-        Construct the lagrangian relaxation of an equality constrained quadratic function defined as:
-
-                                1/2 x^T Q x + q^T x : A x = 0
-
-        By using Lagrange multipliers and seeking the extremum of the Lagrangian, it may be readily
-        shown that the solution to the equality constrained problem is given by the linear system:
-
-                                | Q A^T | |    x   | = | -q |
-                                | A  0  | | lambda |   |  0 |
-
-        where lambda is a set of Lagrange multipliers which come out of the solution alongside x.
-
-        :param A: equality constraints matrix to be relaxed
-        """
-        A = np.atleast_2d(np.asarray(A, dtype=np.float))
-        Q = np.vstack((np.hstack((Q, A.T)),
-                       np.hstack((A, np.zeros((A.shape[0], A.shape[0]))))))
-        q = np.hstack((-q, np.zeros(A.shape[0])))
-        super().__init__(Q, q)
-
-
 class LagrangianConstrainedQuadratic(Quadratic):
 
     def __init__(self, quad, A, ub):
@@ -127,7 +102,7 @@ def __init__(self, quad, A, ub):
         # of Q because it is symmetric but could be not positive definite.
         # This will be used at each iteration to solve the Lagrangian relaxation.
         self.L, self.D, self.P = ldl(self.Q)
-        self.A = np.atleast_2d(np.asarray(A, dtype=np.float))
+        self.A = np.asarray(A, dtype=np.float)
         if any(u < 0 for u in ub):
             raise ValueError('the lower bound must be > 0')
         self.ub = np.asarray(ub, dtype=np.float)